An electrochemical system is a system that either derives electrical energy from chemical reactions, or facilitates chemical reactions through the introduction of electrical energy. An electrochemical system generally includes a cathode, an anode, and an electrolyte, and is typically complex with multiple heterogeneous subsystems, multiple scales from nanometers to meters. Examples of these systems include fuel cells, batteries, and electroplating systems. On-line characterization of batteries or fuel cells in vehicles is difficult, due to very rough noisy environments.
On-line characterization of such electrochemical systems is desirable in many applications, which include real-time evaluation of in-flight batteries on a satellite or aviation vehicle, and dynamic diagnostics of traction batteries for electric and hybrid-electric vehicles. In many battery-powered systems, the efficiency of batteries can be greatly enhanced by intelligent management of the electrochemical energy storage system. Management is only possible with proper diagnosis of the battery states.
Although there may be many kinds of characterization models for an electrochemical system, equivalent circuit models are most appropriate in many applications where stringent real-time requirements and limiting computing powers need to be considered. An algorithm for a circuit model is relatively simple, meaning that simulation time is short and the computation cost is relatively low. A circuit model is an empirical model that describes the electrochemical system with a resistor-capacitor (or resistor-inductor-capacitor) circuit.
In a suitable circuit model, major effects of thermodynamic and kinetic processes in the electrochemical system can be represented by circuit elements. For example, the electrode potential between the cathode and the anode of a system can be represented with a voltage source, the charge-transfer processes can be represented with charge-transfer resistances, the double-layer adsorption can be represented with capacitances, and mass-transfer or diffusion effects can be represented with resistances such as Warburg resistances. Therefore a circuit model is extremely useful for many on-line diagnostics of the real-time states of an electrochemical system.
There are several types of algorithms for a circuit model. These algorithms include parametric regression of circuit analog, Kalman filter, fuzzy logic, pattern recognition, and impedance spectroscopy. Of these algorithms, parametric regression of circuit analog and Kalman filters may have difficulties in describing non-linear parameters in an electrochemical system, such as the Warburg resistance. Fuzzy logic and pattern recognition are not reliable and practical because they are less relevant to a physical description of the system. Impedance spectroscopy is a relatively mature algorithm and is extensively used in lab equipment, but is less useful for on-line real-time characterization because it needs relatively long time (on the order of minutes).
Prior methods include those described in Xiao et al., “A universal state-of-charge algorithm for batteries,” 47th IEEE Design Automation Conference, Anaheim, Calif., 2010. This paper deduces the impulse response for state of charge estimation of batteries. The model was simply a superposition of a constant voltage source and a linear circuit box characterized by an impulse response function. However, the algorithm is not robust against signal noises, and therefore is limited in on-line applications.
Other prior methods include those described in U.S. Pat. No. 7,015,701, issued to Wiegand and Sackman; U.S. Pat. No. 6,339,334, issued to Park and Yoo; U.S. Pat. No. 7,504,835, issued to Byington et al.; and U.S. Pat. No. 5,633,801, issued to Bottman. These patents describe methods to measure electrochemical impedance in the time domain. These patents disclose different time signals for exciting the detected electrochemical systems. Wiegand and Sackman disclose frequency-rich alternating current signals, Park and Yoo disclose differential delta functions, Byington et al. disclose broadband alternating current signals, and Bottman discloses short pulse signals. These patents do not disclose techniques to address data noise and other real-time, on-line challenges.
In view of the shortcomings in the art, improved algorithms for characterizing electrochemical systems are needed. These algorithms, and the apparatus and systems to implement them, preferably are able to broadly accept various exciting signals, are stable and robust against noises, and are agile for real-time use. In practical applications, noise must be addressed in order to deduce an impulse response through one or more noise-reduction techniques. The impulse response should then enable characterization of various states (beyond impedance) of the electrochemical system.